Answer:The length of the shortest piece is [tex]1\textrm{ ft}[/tex].The length of the medium-sized piece is [tex]3\textrm{ ft}[/tex].The length of the longest piece is [tex]7\textrm{ ft}[/tex].Step-by-step explanation:The five-step method is GUESS method.Given:Length of copper wire, [tex]L=11\textrm{ ft}[/tex]Length of longest piece is 6 feet longer than the shortest one.Length of the medium-sized piece is 3 times the shortest one.Unknown:Length of longest, medium-sized and shortest pieces of wire.Let the length of shortest piece be [tex]x[/tex] feet.Therefore, the length of longest piece is equal to [tex]6+x[/tex].And, length of the medium-sized piece is equal to [tex]3x[/tex].Evaluate:Sum of lengths of longest, medium-sized and shortest pieces of wire is equal to the total length of wire. So,[tex]6+x+x+3x=11\\5x+6=11\\5x=11-6\\5x=5\\x=\frac{5}{5}=1[/tex]Substitute and Solve:Now, we have, [tex]x=1[/tex].Substitute 1 for [tex]x[/tex] and solve for each sizes of wire pieces. This gives,Length of shortest piece = [tex]x=1\textrm{ ft}[/tex]Length of medium-sized piece = [tex]3x=3(1)=3\textrm{ ft}[/tex]Length of longest piece = [tex]6+x=6+1=7\textrm{ ft}[/tex]Therefore, the lengths of shortest, medium-sized, and longest pieces are [tex]1\textrm{ ft}[/tex], [tex]3\textrm{ ft}[/tex] and [tex]7\textrm{ ft}[/tex] respectively.